Indefinite Integrals

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What is an indefinite integral?

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An indefinite integral represents a family of functions whose derivative is the integrand. It is expressed as \( \int f(x) \, dx = F(x) + C \), where \( F(x) \) is the antiderivative of \( f(x) \) and \( C \) is the constant of integration.

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What is the power rule for integration?

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The power rule states that for any real number \( n \neq -1 \), \( \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \).

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What is the constant multiple rule in integration?

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The constant multiple rule states that \( \int k \, f(x) \, dx = k \int f(x) \, dx \), where \( k \) is a constant.

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What is the integral of \( e^x \)?

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The integral of \( e^x \) is \( \int e^x \, dx = e^x + C \).

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What is the integration of \( \sin(x) \)?

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The integral of \( \sin(x) \) is \( \int \sin(x) \, dx = -\cos(x) + C \).

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